The director of Science Museum Group told BBC Radio 4 that "one of our three great northern museums" would almost certainly have to close its doors. Photograph: PA

The Science Museum Group may be forced to shut one of its regional museums as a result of the government's squeeze on budgets, its director has claimed. In addition to major cuts in funding for the Science Museum in London, Ian Blatchford said one of the group's outposts may have to close its doors.

The group runs the Museum of Science and Industry in Manchester, the National Railway Museum in York and Bradford's National Media Museum. Blatchford said the prospect of a further 10% cut in funding meant that one of these would almost certainly have to go.

Blatchford told BBC Radio 4's World at One: "There are two problems. The first is we are already in quite a weak position because in the existing spending round we ended up with 25% real-terms cuts. But the real problem is there seems a very strong prospect of a further 10% of cuts which basically means that we will end up with a deficit, currently of £2m, rising to about £6m a year which for a museum is a huge amount of money."

Asked if that would mean the closure of a museum, he said: "I have to say, with a very heavy heart, it really does. We have done lots of boring and sensible things, awful things like cutting staff, procurement, raising more money. But cuts of that level bite really deep into our flesh so it means not only big cuts in the Science Museum in London but that one of our three great northern museums almost certainly [will] also have to close."

National museums do not charge for admission, but Blatchford said he was in talks with the government about the possibility of reinstating entry fees.

"Even though it might be an option, it's certainly not an option on the table at the moment, I just don't have the power to do it," he said. "It's part of the conversation we are having with them because, clearly, we appreciate times are tough and they also do appreciate that if the cuts are significant there will be some pain."

A spokesperson at the Department for Culture, Media and Sport said: "It would be inappropriate to speculate on the outcome of the Spending Review. This is an operational matter for the Science Museum Group [which] has to address a large projected operating deficit from 2014 onwards and is assessing a range of options to address this situation."